Operators of polaroid type and perturbation theory (Q2906221)

The paper is based on earlier results of the first author, devoted to similar problems. The authors consider subclasses of quasi-Fredholm operators called: polaroid, \(a\)-polaroid, left polaroid and right polaroid. They prove that, if a bounded linear operator is left or right polaroid, then it is polaroid (Theorem 2.5) and, if each restriction of operator \(T\) to the closed invariant subspace of its domain is polaroid, then \(T+K\) is polaroid and \(T'+K'\) is \(a\)-polaroid, where \(K\) is an operator commuting with \(T\) and \(T',K'\) are the respective dual operators (Theorem 2.12). Additionally, the paper contains some facts cited without proofs from a preprint (see [Stud. Math. 214, No. 2, 121--136 (2013; Zbl 1278.47007)]) by the same authors.